Theory of Soret Coefficients in Binary Organic Solvents Semen Semenov* ,† and Martin Schimpf ‡ † Institute of Biochemical Physics RAS, Kosygin St. 4, 119334 Moscow, Russia ‡ Department of Chemistry, Boise State University, Boise, Idaho 83725, United States ABSTRACT: Thermodiffusion in binary molecular liquids is examined using the nonequilibrium thermodynamic model, where the thermodynamic parameters are calculated using equations based on statistical mechanics. In this approach, thermodiffusion is quantified through the variation in binary chemical potential and its temperature and concentration dependence. The model is applied to solutions of organic solvents, in order to compare our theoretical results to experimental results from the literature. A measurable contribution of the orientation-dependent Keezom interaction is shown, where the possible orientations are averaged using the Boltzmann weighting factor. Calculations of enthalpies of evaporation from the model yield good agreement with experimental values from the literature. However, calculations of the associated energetic parameters were several times larger than those reported in the literature from numeric simulations of material transport. ■ BACKGROUND Recent attempts to explain thermodiffusion (the Soret effect) in organic liquid mixtures using models based on nonequilibrium thermodynamics and equilibrium statistical thermodynamics have been a topic of discussion in the literature. Such models are based on the temperature and concentration dependence of the chemical potentials of the components μ i , as outlined below. The material flux J ⃗ i in a nonhomogeneous and nonisothermal mixture can be defined as 1,2 μ ⃗ =− ∇ − ∇ J nL T nL T 1 i i i i i iQ (1) where n i are the numeric volume concentrations of the components, L i and L iQ are the Onsager coefficients, and T is the temperature. The material transport parameters are expressed through the temperature and concentration depend- ence of the binary chemical potential: 2−5 μ μ μ *= − v v 2 2 1 1 (2) where v i are the specific molecular volumes of the respective components. For ease of reading, we will subsequently refer to component 1 as the “solvent” and component 2 as the “solute”, although the model applies to the entire concentration range. The last term in eq 2 is the free energy of the solvent molecules displaced from the volume occupied by the solute. We refer to this parameter as the chemical potential of a virtual particle consisting of the solvent but having the same shape and dimensions as the solute. The final expressions 2−5 use the Gibbs−Duhem equation to express the binary chemical potential through the (nonuniform) excess pressure P osm as follows: δμ ϕ δ δμ * = − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ v P v 2 s s (3) Here δ indicates the difference in the parameter between the hot and cold reservoirs, μ s and v s are the chemical potential and specific molecular volume of the solvent, respectively, P is the total pressure, and ϕ is the volume fraction of the solute. The parameter δμ s /ν s is interpreted as the difference in the pure- solvent partial pressure between hot and cold reservoirs, and eq 3 is rewritten as 2−5 δμ ϕ δ * = v P 2 osm (4) The same general approach is used by Morozov. 6 The issue related to any approach that expresses parameters of mass and thermodiffusion through pressure becomes obvious from the statistical−mechanical expressions for pressure and chemical potential: 7,8 =− ∂ ∂ P kT V Z ln (5) μ =− ∂ ∂ kT N Z ln i i (6) Here V is the volume of the system, N i is the number of particles of type i, and Z is the partition function. Statistical mechanical models typically begin with the chemical potential of a component as an ideal gas: 7,8 Received: October 28, 2013 Revised: February 17, 2014 Published: February 18, 2014 Article pubs.acs.org/JPCB © 2014 American Chemical Society 3115 dx.doi.org/10.1021/jp410634v | J. Phys. Chem. B 2014, 118, 3115−3121